A new multi-harmonic statistic for the detection of steady-state evoked potentials

We consider the problem of detecting visual evoked potentials (VEPs) obtained at near-threshold stimulus levels. A new multi-harmonic based statistic (Generalized T/sub circ//sup 2/) is derived. This statistic, denoted by GT/sub circ//sup 2/, is based on the same assumptions concerning the variability of a Fourier component that are made in the use of the T/sub circ//sup 2/ statistic. However, unlike the T/sub circ//sup 2/ statistic which only treats a single harmonic, the GT/sub circ//sup 2/ statistic performs a multi-harmonic analysis which is more suitable for detecting multi-harmonic VEPs. A complete theoretical analysis for the derivation of the (GT/sub circ//sup 2/) statistic is presented as a function of the likelihood ratio criterion, and its distribution is found under the H/sub 0/ hypothesis.